Reflection From Free Surface of a Rotating Generalized Thermo-Piezoelectric Solid Half Space
الموضوعات :
1 - Department of Mathematics, Post Graduate Government College, Sector-11, Chandigarh, 160011,India
2 - Department of Applied Sciences, Rayat Bahra Institute of Engineering and Nano Technology, Hoshiarpur, 146001, Punjab, India
الکلمات المفتاحية: Rotation, Reflection, Plane waves, Thermo-piezoelectric, Reflection coefficients,
ملخص المقالة :
The analysis of rotational effect on the characteristics of plane waves propagating in a half space of generalized thermo-piezoelectric medium is presented in context of linear theory of thermo-piezoelectricity including Coriolis and centrifugal forces. The governing equations for a rotating generalized thermo-piezoelectric medium are formulated and solved for plane wave solutions to show the propagation of three quasi plane waves in the medium. A problem on the reflection of these plane waves is considered from a thermally insulated/isothermal boundary of a rotating generalized thermo-piezoelectric solid half space. The expressions for reflection coefficients of three reflected waves are obtained in explicit from. For experimental data of LiNbO3 and BaTiO3, the speeds of various plane waves are computed. The reflection coefficients of various reflected waves are also obtained numerically by using the data of BaTiO3. The dependence of speeds of plane waves and reflection coefficients of various reflected waves is shown graphically on the rotation parameter at each angle of incidence.
[1] Abd-alla A.N., Alsheikh F.A., 2009, Reflection and refraction of plane quasi longitudinal waves at an interface of two piezoelectric media under initial stresses, Archive of Applied Mechanics 79(9): 843-857.
[2] Abd-alla A.N., Hamdan A.M., Giorgio I., Vescova D.D., 2014, The mathematical model of reflection and refraction of longitudinal waves in thermo-piezoelectric materials, Archive of Applied Mechanics 84(9): 1229-1248.
[3] Alshit V.I., Lothe J., Lyubimov V.N., 1984, The phase shift for reflection of elastic waves in hexagonal piezoelectric crystals, Wave Motion 6: 259-264.
[4] Alshits V.I., Shuvalov A.L., 1995, Resonance reflection and transmission of shear elastic waves in multilayered piezoelectric structures, Journal of Applied Physics 77(6): 2659-2665.
[5] Auld B.A., 1981, Wave propagation and resonance in piezoelectric materials, Journal of Acoustical Society of America 70(6): 1577-1585.
[6] Burkov S.I., Sorokin B.P., Aleksandrov K.S., Karpovich A.A., 2009, Reflection and refraction of bulk acoustic waves in piezo electrics under uniaxial stress, Acoustical Physics 55(2): 178-185.
[7] Cady W.G., 1946, Piezoelectricity, McGraw-Hill, New York.
[8] Chandrasekharaih D.S., 1984, A temperature rate dependent theory of piezoelectricity, Journal of Thermal Stresses 7: 293-306.
[9] Chen J.Y., Chen H.L., Pan E., 2008, Reflection and transmission coefficients of plane waves in magneto-electro-elastic layered structures, Journal of Vibration and Acoustics 130: 031002.
[10] Clezio E.L., Shuvalov A., 2004, Transmission of acoustic waves through piezoelectric plates: Modeling and Experiment, IEEE Ultrasonics Symposium 1: 553-556.
[11] Darinskii A.N., Clezio E.L., Feuillard G., 2008, The role of electromagnetic waves in the reflection of acoustic waves in piezoelectric crystals, Wave Motion 45(1): 428-444.
[12] Dunn M. L., 1993, Micromechanics of coupled electro-elastic composites: effective thermal expansion and pyroelectric coefficients, Journal of Applied Physics 73: 5131-5140.
[13] Eringen A.C., Maugin G.A., 1990, Electrodynamics of Continua: I Foundations and Solid Media, Springer Verlag, New York.
[14] Every A.G., Neiman V.I., 1992, Reflection of electroacoustic waves in piezoelectric solids: Mode conversion into four bulk waves, Journal of Applied Physics 71(12): 6018-6024.
[15] Green A.E., Lindsay K.A., 1972, Thermoelasticity, Journal of Elasticity 2: 1-7.
[16] Ikeda T., 1996, Fundamentals of Piezoelectricity, Oxford Science Publications, Oxford University Press.
[17] Kuang Z.B., Yuan X.G., 2011, Reflection and transmission of waves in pyroelectric and piezoelectric materials, Journal of Sound and Vibration 330(6): 1111-1120.
[18] Kaung Z. B., 2013, Theory of Electroelasticity, Springer.
[19] Lord H., Shulman Y., 1967, A generalised dynamical theory of thermoelasticity, Journal of Mechanics and Physics of the Solids 15: 299-309.
[20] Lothe J., Barnett D.M., 1976, Integral formalism for surface waves in piezoelectric crystals: Existence considerations, Journal of Applied Physics 47: 1799-1807.
[21] Maugin G.A., 1988, Continuum Mechanics of Electromagnetic Solids, Elsevier Science Publishers, Amsterdam, New York, Oxford.
[22] Mindlin R.D., 1972, High frequency vibrations of piezoelectric crystal plates, International Journal of Solids and Structures 8(7): 895-906.
[23] Mindlin R.D., 1974, Equations of high frequency vibrations of thermo-piezoelectric crystal plates, International Journal of Solids and Structures 10(6): 625-637.
[24] Nayfeh A.H, Chien H.T., 1992, The influence of piezoelectricity on free and reflected waves from fluid loaded anisotropic plates, Journal of Acoustical Society of America 91(3): 1250 -1261.
[25] Noorbehesht B., Wade G., 1980, Reflection and transmission of plane elastic waves at the boundary between piezoelectric materials and water, Journal of Acoustical Society of America 67(6): 1947-1953.
[26] Nowacki W., 1978, Some general theorems of thermo-piezo-electricity, Journal of Thermal Stresses 1: 171-182.
[27] Pal A.K., 1979, Surface wave in a thermo-piezoelectric medium of monoclinic symmetry, Czechslovak Journal of physics 29: 1271-1281.
[28] Pang Y., Wang Y.S., Liu J.X., Fang D.N., 2008, Reflection and refraction of plane waves at the interface between piezoelectric and piezo magnetic media, International Journal of Engineering Science 46(11): 1098-1110.
[29] Parton V.Z., Kudryavtsev B.A., 1988, Electromagnetoelasticity: Piezo electrics and Electrically conductive Solids, Gordon and Beach, New York.
[30] Ponnusamy P., 2016, Elastic waves in generalized thermo-piezoelectric transversely isotropic circular bar immersed in fluid, Advances in Applied Mathematics and Mechanics 8(1): 82-103.
[31] Rosenbaum J.F., 1988, Bulk Acoustic Wave Theory and Devices, Artech House, Boston.
[32] Schoenberg M., Censor D., 1973, Elastic waves in rotating media, Quarterly of Applied Mathematics 31: 115-125.
[33] Sharma J.N., Kumar M., 2000, Plane harmonic waves in piezothermoelastic materials, Indian Journal of Engineering and Material Sciences 7: 434-442.
[34] Sharma J.N., Walia V., 2007, Effect of rotation on Rayleigh waves in piezothermoelastic half-space, International Journal of Solids and Structures 44: 1060-1072.
[35] Shuvalov A.L., Clezio E.L., 2010, Low-frequency dispersion of fundamental waves in anisotropic piezoelectric plates, International Journal of Solids and Structures 47: 3377-3388.
[36] Singh B., 2005, On the theory of generalized thermoelasticity for piezoelectric materials, Applied Mathematics and Computation 171: 398-405.
[37] Singh B., 2010, Wave propagation in a pre-stressed piezoelectric half-space, Acta Mechanica 211: 337-344.
[38] Singh B., 2013, Propagation of shear waves in a piezoelectric medium, Mechanics of Advanced Materials and Structures 20: 434-440.
[39] Tiersten H.F., 1969, Linear Piezoelectric Plate Vibrations, Plenum, New York.
[40] Toupin R.A., 1956, The elastic dielectric, Archive for Rational Mechanics and Analysis 5: 849-915.
[41] Voigt W., 1910, Lehrbuch der Krystallphysik, Mathematischen Wissenschaften, band XXXIV, Leipzig und Berlin, B.G. Teubner.
[42] Weis R.S., Gaylord T.K., 1985, Summary of physical properties and crystal structure, Applied Physics A 37: 191-203.
[43] Yang J., 2005, An Introduction to the Theory of Piezoelectricity, Springer, New York.
[44] Zhang Q.M., Geng X., Yuan J., 1996, Reflection of plane waves at medium composite interfaces and input acoustic impedance of laminated piezo ceramic polymer composites, Journal of Applied Physics 80(9): 5503-5505.
